Exercise 1.2.15

Question

Let $\mathrm{V}=\left\{\left(a_{1}, a_{2}, \ldots, a_{n}\right): a_{i} \in R\right.$ for $\left.i=1,2, \ldots, n\right\}$; so $\mathrm{V}$ is a vector space over $R$ by Example 1. Is $\mathrm{V}$ a vector space over the field of complex numbers with the operations of coordinatewise addition and multiplication?

Jephian C.-H. Lin · Accepted Answer

No. Because a real-valued vector scalar multiply with a complex number will not always be a real-valued vector.

Exercise 1.2.15

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Exercise 1.2.15

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